If \(W\equiv 1\) , \(\varphi \left( x\right) =x^{p}\) , \(1\le p<\infty \) , on more
general Homogenous Banach spaces this theorem was obtained in [1]}.
When \(1<p<\infty \) , \(W\in A_{p}\) , \(\varphi \left( x\right) =x^{p}\) , \(k=1\) , (REF ) was proved in [2]}, [3]}. For \(k=1\)  see the papers [4]}, [5]}. Under the conditions \(k=1\)  and convex \(\varphi \)  some variant
of (REF ) was obtained in [6]}.
